An investigation of an adaptive modeling algorithm for magnetic resonance image reconstruction

The paper proposes an algorithm for active noise control (ANC) using the least squares lattice (LSL) algorithm. As a main algorithm for ANC, the LMS algorithm has been used for its simplicity. However, the LMS algorithm has problems of both convergence speed and estimation accuracy in the case of the broadband noise such as road noise which is one of the passenger compartment noises in a car running on rough roads. In order to solve these problems, the LSL algorithm for ANC is considered. By computer simulations, the LSL algorithm turns out to be more effective than the LMS algorithm in both convergence speed and estimation accuracy, especially for the colored input signal used in ANC of road noise.

Publication in the conference proceedings of EUSIPCO, Trieste, Italy, 1996

Comparison of the ARMA, ARIMA, and the autoregressive artificial neural network models in forecasting the monthly inflow of Dez dam reservoir

Three important parametric models for describing the correlation functions and spectra of stationary stochastic processes are the autoregressive (AR), moving average (MA), and autoregressive-moving average (ARMA) models. Quite recently, the MATLAB toolbox “ARMASA” has been made publicly available. This toolbox provides state-of-the-art algorithms to perform automatic identification and selection between the models based on the estimated prediction error. ARMASA works on a single segment of data, whereas in some applications, the data are available as multiple segments. We could process each segment independently and average the estimated autocorrelation functions or spectra afterward. Better performance, however, can be expected when all segments are processed simultaneously, for two reasons. Initially, the bias in the estimated model parameters depends on the number of observations in a segment. Averaging models from segments does not reduce this bias, in contrast to identification from all the data at once. In either case, the variance of the estimated model parameters will decrease. By considering all the data at once this variance reduction can be considered in the order selection stage, decreasing the selection bias. In this paper, we extend the parameter estimation algorithms of the ARMASA toolbox to the case of multiple segments. AR parameter estimation from segments has been considered before, but not for the MA and ARMA models. In addition, in the AR case, model order selection can be done easily when the segments are independent. But, in the application we are primarily interested in, the segments are formed by lines of scanning transmission electron microscopy (STEM) images, which can be correlated with each other. Because the correlation among data segments influences the effective number of independent observations available it becomes necessary to estimate that number. This is not an easy problem in general. For observations from a stochastic process with an isotropic 2-D autocorrelation function we can, however, formulate an accurate estimator in terms of the line autocorrelation function. This situation arises, for example, in STEM images of amorphous specimens. From the AR model identification for segments, the extension to the MA and ARMA models is rather straightforward because MA and ARMA algorithms are based on Durbin's methods, whose first step is the estimation of a long AR model. We compare the segment-based algorithms to conventional ARMASA with simulations of stationary stochastic processes. An illustrative example involving simulated STEM images shows large potential benefits.

To investigate feasibility of applying deep learning image reconstruction (DLIR) algorithm in a low-kilovolt enhanced scan of the upper abdomen. A total of 64 patients (BMI<28) are selected for the enhanced upper abdomen scan and divided evenly into two groups. The tube voltages in Group A are 100kV in arterial phase and 80kV in venous phase, while tube voltages are 120kV during two phases in Group B. Image reconstruction algorithms used in Group A include the filtered back projection (FBP) algorithm, the adaptive statistical iterative reconstruction-Veo (ASIR-V 40% and 80%) algorithm, and the DLIR algorithm (DL-L, DL-M, DL-H). Image reconstruction algorithm used in Group B is ASIR-V40%. The different reconstruction algorithm images are used to measure the common hepatic artery, liver, renal cortex, erector spinae, and subcutaneous adipose in the arterial phase and the average CT value and standard deviation of the portal vein, liver, spleen, erector spinae, and subcutaneous adipose in the portal phase. The signal-to-noise ratio (SNR) is calculated, and the images are also scored subjectively. In Group A, noise in the aorta, liver, portal vein (the portal phase), spleen (the portal phase), renal cortex, retroperitoneal adipose, and muscle is significantly lower in both the DL-H and ASIR-V80% images, and the SNR is significantly higher than those in the remaining groups (P<0.05). The SNR of each tissue and organ in Group B is not significantly different from that in DL-M, DL-L, and ASIR-V40% in Group A (P>0.05). The subjective image quality scores in the DL-H and B groups are higher than those in the other groups, and the FBP group has significantly lower image quality than the remaining groups (P<0.05). For upper abdominal low-kilovolt enhanced scan data, the DLIR-H gear yields a more satisfactory image quality than the FBP and ASIR-V.

Spectral Phase Based Medical Image Processing 1

SIRF: Synergistic Image Reconstruction Framework

In this paper, we proposed a new method able to select, simultaneously, from finite length time-series sequence, the suitable model type; pure Autoregressive (AR) or Autoregressive Moving Average (ARMA), which best describes the process that generated data. This is also a new way for estimating ARMA model order. The proposed method is different in its concept from all other methods found in the literature, direct and far simpler to implement. We proposed new empirical criteria basing on specific AR order selection criteria for finite length time series. We tested the proposed criteria on 10000 realizations of different broadband and narrow band processes. We also studied effects of additive noise and data length on their performance. The best mean recognition rate of model type was 92%. [Formula: see text]-value of Fisher’s exact test was always strictly under [Formula: see text]. Power spectral densities of selected models managed to recover the true Power spectral density (PSDs) shapes by resolving close spectral peaks and by finding their positions and their bandwidths with negligible spectral biases. Efficiency of our method was proved by its application in automatic segmentation of electrohysterographic signals (EHG) in the aim of predicting preterm deliveries with a mean rate of 90%.

The determination of autoregressive (AR) and autoregressive moving average (ARMA) algorithms for simulating realizations of two-dimensional random fields with a specified (target) power spectrum is examined. The form of both of these models is justified first by considering infinite-variate vector processes of appropriate spectral matrix. Next, the AR parameters are selected to achieve the minimum of a positive integral. Then, a technique is formulated to derive an ARM A simulation algorithm from the prior AR approximation by relying on the minimization of frequency domain errors. Finally, these procedures are critically assessed and an example of application is presented.

Objective To establish an autoregression moving average (ARMA) model for predicting general traffic accidents and analyzing distributional difference on time series and frequency of common traffic accident so as to provide certain basis for a prediction model with better stability and accuracy. Methods The data of road traffic accidents in one newly developed zone of Chongqing in 2000-2005 were collected. The monthly distribution regularity of road traffic accidents was analyzed with descriptive epidemiologic method. ARMA model was set up for retrospective and prospective prediction. The predicted data were compared. Results Based on the characteristics of monthly distribution, the frequency of general traffic accidents in this area showed a cyclic fashion. The frequency of general traffic accidents predicted by ARMA model had over 80% of coincidence with the actual value. Conclusion The ARMA model can be used to predict the frequency of general traffic accidents, with better accuracy of short-term prediction than the long-term prediction. Key words: Accidents, traffic; ARMA; Time series; Prediction model

Computed tomography (CT) relies on computational algorithms to reconstruct images from CT projections. Current filtered backprojection reconstruction methods have inherent limitations in situations with sharp density gradients and limited beam views. In this thesis two novel reconstruction algorithms were introduced: the Algebraic Image Reconstruction (AIR) algorithm, and the Geometric Image Reconstruction Algorithm (GIRA). A CT simulation was developed to test these novel algorithms and compare their images to filtered backprojection images. AIR and GIRA each demonstrated their proof of principle in these preliminary tests. AIR and its extension, the Parsed AIR algorithm (PAIR), were able to reconstruct optimal images compared to filtered backprojection after empirically determining parameters relevant to the algorithms. While GIRA reconstructed optimal images in preliminary tests, reconstruction was complicated by error propagation for larger imaging domains. The initial success of these novel approaches justifies continued research and development to determine their feasibility for practical CT image reconstruction.

The problem of estimating the autoregressive (AR)-order and the AR parameters of a causal, stable, single input single output (SISO) autoregressive moving average (ARMA) (p,q) model, excited by an unobservable i.i.d. process, is addressed. The observed output is corrupted by additive colored Gaussian noise, whose power spectral density is unknown. The ARMA model may be mixed-phase, and have inherent all-pass factors and repeated poles. It is shown that consistent AR parameter estimates can be obtained via the normal equations based on (p+1) 1-D slices of the mth-order (m>2) cumulant. It is shown via a counterexample that consistent AR estimates cannot, in general, be obtained from a subset of these p+1 slices. Necessary and sufficient conditions for the existence of a full-rank slice are also derived.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

3D or multi-dimensional medical image reconstruction is attracting more and more attention in modern era. Rapid volumetric image reconstruction is of paramount importance to clinicians for prompt diagnosis and analysis of complex tissue alternations. However, due to a high demand on computation for either the analytical or iterative image reconstruction algorithms, it is almost impossible to meet the requirement of real-time reconstruction. On the other hand, with high computing capability and broad banding characteristic, recently multi-core processors provide a new possibility and hopeful start for some of the most computation-demanding applications, such as medical imaging, digital media and entertainment equipment. This study aims to parallelize an analytical 3D CT image reconstruction algorithm, the so-called FDK method, and to implement it on an existing multi-core platform system, towards a real-time 3D medical image reconstruction. In this paper, the parallelization of the 3D image reconstruction algorithm, the coding optimizations and a comparative result of run time savings are described.

Under appropriate conditions, stochastic processes are described by the ARMA model, however, the AR model is popularly used in reactor noise analysis. Hence, the properties of AR model as an approximate representation of the ARMA model should be made clear. Here, convergence of AR-parameters and PSD of AR model were studied through numerical analysis on specific examples such as the neutron noise in subcritical reactors, and it was found that: 1. The convergence of AR-parameters and AR model PSD is governed by the "zero nearest to the unit circle in the complex plane" (μ−1,|μ|<1) of the ARMA model transfer function.2. The AR-parameters of AR(M) model have biases from those for the infinite model order, and these biases decrease approximately in proportion to |μ|M.3. The AR model of the neutron noise of subcritical reactors needs a large model order because of an ARMA-zero very close to unity corresponding to the decay constant of the 6-th group of delayed neutron precursors.4. In applying AR model for system identification, much attention has to be paid to a priori unknown error as an approximate representation of the ARMA model in addition to the statistical errors.

Low-dose computed tomography (CT) has attracted much attention in clinical applications since X-ray radiations can cause serious health risks to patients. Sparse-view CT imaging is one of the major ways to reduce radiation dose. However, if reconstructing the sparse-view CT images with conventional filtered backprojection (FBP) algorithm, image quality may be significantly degraded due to the severe streaking artifacts. Therefore, iterative sparse-view CT image reconstruction (IR) algorithms have been developed and utilized to improve image quality. One drawback of using the IR algorithms is they usually spend long computation time. Additionally, adjusting and optimizing the hyper-parameters that are needed during iteration procedures is also time-consuming, some- times may even depend on individual experience. These potential drawbacks strongly limit the wide applications of IR algorithms. Aiming at partially overcome such difficulties, in the present work, we propose a deep iterative reconstruction (DIR) framework to generalize the conventional IR algorithms by mapping them into the deep neural network (DNN) technique. With this proposed DIR algorithms, the prior term, the data fidelity term, and the hyper-parameters can all be represented and learned by network. By doing so, some generalized iterative models can be used to perform high quality sparse-view CT image reconstructions. Numerical experiments based on clinical patient data demonstrated that the proposed DIR algorithms can mitigate the streaking artifacts more effectively while well preserving the subtle structures.